考虑弹性水击效应时水轮机调节系统的Hopf分岔分析  

Hopf bifurcation analysis of hydraulic turbine governing systems with elastic water hammer effect

作　　者：凌代俭[1] 陶阳[1] 沈祖诒[2] 

机构地区：[1]扬州大学建筑科学与工程学院,江苏扬州225009 [2]河海大学水利水电工程学院,江苏南京210098

出　　处：《振动工程学报》2007年第4期374-380,共7页Journal of Vibration Engineering

摘　　要：在考虑水轮机调节系统中弹性水击效应的情况下,建立了系统的非线性模型,在此基础上,运用非线性动力系统的分岔理论分别研究了在频率扰动、负荷扰动或无扰动的情况下,由于PID调节器参数发生变化,在系统中可能发生的Hopf分岔现象,在PID参数空间中给出了分岔临界点、稳定域范围以及状态变量随分岔参数变化的分岔图,并与刚性水击情况进行了比较。由此得出结论,由于调节器参数的变化,在水轮机调节系统中可能导致所不期望的持续非线性振荡,为保证系统能够安全稳定地运行,应将调节器参数设定在其稳定域范围内。仿真验证了理论分析的结果。A nonlinear model of hydraulic turbine governing systems with elastic water hammer effect is presented. Based on the model, in the cases of frequency disturbance, load disturbance and without disturbance, bifurcation theories of dynamical systems are applied to analyze the Hopf bifurcation phenomena in the systems with the change of PID regulator parameters. The critical points of Hopf bifurcation, stable regions and bifurcation diagrams are obtained in the PID parameter spaces. The results are in comparison with those of non-elastic water hammer effect. In conclusion, with the varieties of PID parameters, the unexpected and sustained oscillation may appear in hydraulic turbine governing systems. For the sake of safety and stability, the regulator parameters should be set in the stable regions of parameter spaces. The simulations verify the results of the paper.

关 键 词：水轮机调节系统 弹性水击 非线性模型 PID控制 HOPF分岔 

分 类 号：TV734.4[水利工程—水利水电工程] O322[理学—一般力学与力学基础]